about the age and arthritis factors. You need to space your day with alternating between rides, shows, parades, fireworks, exhibits, live street entertainment, and eating. Eating is a great rest period. Shows are good rest periods. By alternating you will find your mom will have a lot more stamina. My 89 year old mother who has a lot of issues can last 8 to 10 hours in a park, as long as, it's not cold or raining. Believe it or not, you can take a nap in the first aid stations that's available in each park, if need be. I would tackle the harder rides early.
Some rides can be tough; because, you need to step down to get in and up to get out (like boat rides). On those ocassions I highly suggest someone going in before her to help her in and someone be behind her just in case she loses her balance, etc. Going out you give her a helping hand out and the one behind again is there for support. When there isn't room for three, one can still be behind and then go on another vehicle for the ride and help when the ride is over, as well. We did this with my mother-in-law who was 90 at the time; it works.
Keep in mind, your mom may need to use a restroom more; so, give her ample opportunities for it. Some restrooms are hard to spot like those in World Showcase at Epcot. You don't want to be caught in an awkward situation waiting in a long ride queue or whatever with the urge to go.
There are some rides where you can transfer into a wheelchair and the wheelchair can go right onto the ride where the scooter cannot. Example of this is It's a Small, Small World in MK. You will have to get a cast member involved; so, they can arrange to get a wheelchair.
There may be some rides she just doesn't want to go on in which case I think someone should keep her company while the others enjoy the ride. I wouldn't do too many roller coaster rides with her, as an example. Do a little shopping or grab a snack, etc. while others enjoy some of the rides without her. Prepare the family as a whole that there will be some comprises on this trip with grandma coming; you never want grandma to feel unwanted or that she is a burden to anyone.
Scooters are allowed access to handicap areas for shows and parades. These areas fill up fast; so, get there early. For restaurants you will have to park your scooter outside in most cases. Make sure you park where you don't interfere with entrances, etc.
Have your mom practice a little at home by using a free scooter at the grocery store, etc. Scooters at the parks have their challenges. You will be going through some sharp turns in ride queues. Have your party break up with some in front of your mom and some in back of your mom; keep her in the middle of your group. Parking a scooter in some tight spaces for the rides, etc. is challenging,too; so, it may be better for someone else to park the scooter. It will be faster to do it this way, as well. If you are on site using the buses with a scooter, it may be better for someone else to get the scooter in position on the bus The parks can be very crowded especially with you not utilizing early hours at the parks. You will have people (kids and adults) that will dart out in front of a scooter whereas your mom will have to stop fast or swing left or right to avoid hitting these people. Believe me, a horn really doesn't work in these episodes. Some scooters (especially the smaller ones) don't have headlights. We actually bring our own bike lights to mount on a rental scooter. At night the headlights help others to see you and it also helps you in some of the darker places of the park to navigate better. There are lights at the parks, but some areas can still be rather dark. If you stay until closing and use the buses (or monorail) to get to your Disney resort I would let the crowds get out before going myself. You don't have to be the last one out, but let the park thin out some. Also, be aware scooters can't jump curbs. You need to follow the same pathways as a wheelchair. Always remember to take your valuables with you when you leave your scooter for whatever reasons (including restroom) and take the key to the scooter, too.
Have a great trip with your mom.